We present a framework for understanding how the hippocampus, neocortex, and basal ganglia work together to support cognitive and behavioral function in the mammalian brain. This framework is based on computational tradeoffs that arise in neural network models, where achieving one type of learning function requires very different parameters from those necessary to achieve another form of learning. For example, we dissociate the hippocampus from cortex with respect to general levels of activity, learning rate, and level of overlap between activation patterns. Similarly, the frontal cortex and associated basal ganglia system have important neural specializations not required of the posterior cortex system. Taken together, this overall cognitive architecture, which has been implemented in functioning computational models, provides a rich and often subtle means of explaining a wide range of behavioral and cognitive neuroscience data. Here, we summarize recent results in the domains of recognition memory, contextual fear conditioning, effects of basal ganglia lesions on stimulus-response and place learning, and flexible responding.